This chapter attempts to give a brief overview of nonclassical (-logic) theories of truth. Due to space limitations, we follow a victory-through-sacrifice policy: sacrifice details in exchange for clarity of big-picture ideas. This policy results in our giving all-too-brief treatment to certain topics that have dominated discussion in the non-classical-logic area of truth studies. (This is particularly so of the ‘suitable conditoinal’ issue: §4.3.) Still, we present enough representative ideas that one may fruitfully turn from this essay to the more-detailed (...) cited works for further study. Throughout – again, due to space – we focus only on the most central motivation for standard non-classical-logic-based truth theories: namely, truth-theoretic paradox (specifically, due to space, the liar paradox). (shrink)

This dissertation is a critical examination of dialetheism, the view that there are true contradictions. Dialetheism's proponents argue that adopting the view will allow us to solve hitherto unsolved problems, including the well-known logical paradoxes. ;Dialetheism faces three kinds of challenge. Challenges of the first kind put in doubt the intrinsic coherence of dialetheism. It can be claimed, for example, that it is incoherent for a claim to be both true and false; that claims known to be false cannot be (...) accepted; that claims known to be false cannot be rationally accepted; and that dialetheism entails the falsity of some of its own theoretical claims. The second kind of challenge concerns the use of paraconsistent logics, which dialetheists must adopt on pain of accepting the truth of every proposition. I examine a number of paraconsistent logics, and conclude that either they come at an unacceptably high price or they do not support the dialetheist project. ;I devote most attention to the third kind of challenge, according to which dialetheism fails to provide the promised solutions to the paradoxes and other previously intractable problems, and so we lose the major motivation for the theory. Proponents claim that dialetheism allows for the solution of numerous problems, particularly in metaphysics, law, and logic. In the case of metaphysics, it is claimed that dialetheism allows us to deal with puzzles involving change, vagueness, and motion. However, I argue that the proposed solution does not eliminate the old metaphysical problems, and in fact gives rise to new ones. In the case of law, it is claimed that dialetheism can allow us to deal with legal contradiction. I argue there are more plausible means of solving such conflicts. The strongest case for dialetheism is that it allows us to solve logical and semantic paradoxes of self-reference, some of which have endured for well over two thousand years. I construct a paradox that the dialetheist cannot accommodate, and which shows that dialetheism never provided a solution to the paradoxes at all, even in their more familiar forms. (shrink)

In In Contradiction, Graham Priest shows, as clearly as anything like this can be shown, that it is coherent to maintain that some sentences can be both true and false at the same time. As a consequence, some contradictions are true, and an appreciation of this possibility advances our understanding of the nature of logic and language.

Vague predicates, on a paraconsistent account, admit overdetermined borderline cases. I take up a new line on the paraconsistent approach, to show that there is a close structural relationship between the breakdown of soritical progressions, and contradiction. Accordingly, a formal picture drawn from an appropriate logic shows that any cut-off point of a vague predicate is unidentifiable, in a precise sense. A paraconsistent approach predicts and explains many of the most counterintuitive aspects of vagueness, in terms of a more fundamental (...) inconsistency. (shrink)

This is an examination of the dialectical structure of deep disagreements about matters not open to empirical check. A dramatic case in point is the Law of Non-Contradiction . Dialetheists are notoriously of the view that, in some few cases, LNC has a true negation. The traditional position on LNC is that it is non-negotiable. The standard reason for thinking it non-negotiable is, being a first principle, there is nothing to negotiate. One of my purposes is to show that the (...) first-principle defence of LNC is inadequate. A second purpose is to argue that it flows from this inadequacy that LNC stands or falls on economic considerations, much in the spirit of Quine's pragmatism about logic generally. This is a tactical victory for dialetheists. It gives them room to make the case against LNC on cost-benefit grounds. As things presently stand, no such case can be considered decisive. But, given that costs and benefits shift with changing circumstances, it is possible that a winning case for the dialetheist may present itself in the future. Notwithstanding the rivalry between consistentists and dialetheists, they share a common opponent. This is trivialism, the doctrine that everything whatever is true. It is an ironic alliance, in as much as the dialetheist's case against the consistentist can be adapted to a defence of trivialism. How damaging this turns out to be depends on the adequacy of the reasons for the dialetheist's rejection of trivialism. My further purpose is to show that the damage is slighter than dialetheists commonly believe. (shrink)

In the first part the paper rehearses the main arguments why to be a dialetheist (i.e. why to assume that some contradictions are true). Dialetheism, however, has been criticised as irrational or self-refutating. Therefore the second part of the paper outlines one way to make dialetheism rational assertable. True contradictions turn out to be both believable and assertable. The argument proceeds by setting out basic principles of assertion and denial, and employing bivalent truth value operators.

One of the few points of agreement to be found in mainstream responses to the logical and semantic problems generated by vagueness is the view that if any modification of classical logic and semantics is required at all then it will only be such as to admit underdetermined reference and truth-value gaps. Logics of vagueness including many valued logics, fuzzy logics, and supervaluation logics all provide responses in accord with this view. The thought that an adequate response might require the (...) recognition of cases of overdetermination and truth value gluts has few supporters. This imbalance lacks justification. As it happens, Jaskowski's paraconsistent discussive logic-a logic which admits truth value gluts-can be defended by reflecting on similarities between it and the popular supervaluationist analysis of vagueness already in the philosophical literature. A simple dualisation of supervaluation semantics results in a paraconsistent logic of vagueness based on what has been termed subvaluational semantics. (shrink)